Question $2(90$ Marks$)$

a$.$ The top of a pile requires placement at E $101\mathrm{.}700,$ N $200\mathrm{.}800$ and driven to RL $50\mathrm{.}5$m $($say for bridge, wharf or jetty construction$).$ A measurement to the current pile top position has been reduced to be at E $102\mathrm{.}4,$ N $201\mathrm{.}300$ and RL $53\mathrm{.}01$m$.$ Calculate the bearing of the line of piles, assuming the pile has been positioned along the line of the piles. Calculate the skew angle of the pile, assuming it is away from the centre$-$line and is to be driven along the skew $($document all working$).(30$ marks$)$

b$.$ A client has approached you about building a rectangular dam to hold a specific volume of water of $9000m^3.$ The client has limited room and proposes a dam base of $30m40m$ and $40m60m$ at the top. If the desired batter slopes at corners for the dam is $2$:$1($rise:run$),$ calculate the depth and volume of the dam $($fully document all working$).(30$ marks$)$

c$.$ A dam features a drop inlet and spillway pipe to discharge the overcapacity water. The elevation of the stilling basin of a dam is $143\mathrm{.}23m.$ The length of the spillway pipe is $110m$ with a slope of $12\%$ and the diameter of $1m.$ If the maximum capacity of the dam sits at $175\mathrm{.}6m,$ calculate the elevation of the drop inlet $($penstock$).(30$ marks$)$